What are the minimum requirements to call something artificial neural network?
If you pick up a textbook on Neural Networks, you'll find that the simplest examples shown are ones that just implement an AND gate or something.  They're trivial, probably fewer lines of code than what you have there.  The bar to be an "artificial neural network" is pretty low... it certainly isn't the case that ANN's must be incredibly complicated with thousands of lines of code, and many layers, or even many "neurons" total.

Basically, if something is setting up at least one "neuron" with multiple inputs, and using some kind of weighting function to generate an output from those inputs, it's a valid ANN. It might be a really simple example of an ANN, but it's still an ANN.

Remember what Geoffrey Hinton says in his Coursera class - (paraphrased) "We don't pretend that the things we're building really work the way the brain does, we're just taking the brain as loose inspiration for an approach that we've found works".